Purpose
Pennyplotter explains loan and mortgage arithmetic, savings and retirement projections, and tax estimators. It does not give personalized advice, quote a rate from a lender, decide creditworthiness, prepare a return, or say what someone can afford or when to claim a benefit. Pages say what they omit. A mortgage page, for example, leaves out taxes, insurance, mortgage insurance, and add-on products unless that page says otherwise.
The payment formula
The mortgage, 15-year comparison, and auto loan pages call calculateLoan. The payoff page uses the same cent interest rule. Refinance break-even divides closing costs by the payment difference from that function. Compound interest and the retirement projection use the monthly future-value formula. The paycheck page uses the 2026 rate tables and basic standard deduction in Revenue Procedure 2025-32, plus employee FICA from IRS Topic 751. Affordability, rent versus buy, HELOC, card payoff, student loans, savings goals, Roth comparisons, inflation, tax brackets, and PMI each call their own tested function. No PMI premium and no CPI index is invented. Annual percentage yield, self-employment tax, capital gains, the Roth IRA limit, required minimum distributions, Social Security factors, debt payoff order, the emergency fund, 529 growth, and the adjustable-rate comparison each call their own tested function. Where a page uses a statutory dollar amount, that amount comes from the source cited on the page. The browser calls those same functions. It does not keep a second copy of a formula.
Payment = P × r / (1 − (1 + r)−n)
- P is the principal, in dollars.
- The annual figure is a nominal rate. The monthly rate r is that percent divided by 1,200. Six percent is 0.005 per month.
- n is the number of monthly payments.
- At a zero rate, the payment is P divided by n.
- This matches the unit rule in Microsoft's PMT documentation: a monthly loan uses the annual rate divided by 12 and the number of years multiplied by 12. PMT's result is principal and interest, not taxes or fees.
Rounding
- The contractual payment is rounded half-up to the cent. The checked values are $200,000 at 6% for 30 years = $1,199.10, and the same loan for 15 years = $1,687.71.
- Each month, interest is the remaining balance in cents times the annual percent, divided by 1,200, rounded half-up to the cent.
- Principal for that month is the contractual payment minus interest. An optional extra payment is added to principal and is not collected beyond what pays the balance off.
- The last payment is the remaining principal plus that month's interest, so the balance ends at $0.00. On a long loan the last payment can differ from the contractual payment by about a dollar because of the cent rounding along the way.
- If the contractual payment would not cover the first month of interest, the calculator stops and says the loan would not amortize.
Examples are not quotes
A page that opens on 6% is using a round number so the arithmetic can be checked. It is not today's average and not a rate available to a reader. Where a public average matters, the page links to it. Freddie Mac's Primary Mortgage Market Survey is linked from the 15-year versus 30-year article for that reason, and the weekly figure is not copied into the form.
Sources
Explanations of mortgages, APR, escrow, mortgage insurance, prepayment, and auto-loan shopping cite the Consumer Financial Protection Bureau or Freddie Mac, and the payment formula cites Microsoft's PMT documentation. Tax, retirement, and benefit pages cite the IRS publication, revenue procedure, notice, or regulation named on that page. Each calculator page lists the links that were read for that page and the date they were accessed. A linked page can change after that date. Pennyplotter does not control those sites and does not treat a third-party page as legal advice. The CFPB says the same about its own general information.
Updates and corrections
Each calculator page shows a last-updated date. A correction to a formula, a cited fact, or a broken source link should be sent to hello@pennyplotter.com with the page address and the passage. Confirmed errors are corrected in the page, and the date moves.
Authorship
Articles are written by Giuseppe Ilarda, who owns the site. He writes the calculators and the explainers, and he checks them before they are published. The author and the reviewer are the same person. That description does not state a credential, a certification, or a professional finance background. The pages are educational estimates, not financial advice.
Advertising
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